{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Function approximation with linear models and neural network\n",
    "* Are Linear models sufficient for approximating transcedental functions? What about polynomial functions?\n",
    "* Do neural networks perform better in those cases?\n",
    "* Does the depth of the neural network matter?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import basic libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global variables for the program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_points = 100 # Number of points for constructing function\n",
    "x_min = 1 # Min of the range of x (feature)\n",
    "x_max = 25 # Max of the range of x (feature)\n",
    "noise_mean = 0 # Mean of the Gaussian noise adder\n",
    "noise_sd = 10 # Std.Dev of the Gaussian noise adder\n",
    "test_set_fraction = 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate feature and output vector for a non-linear function with transcedental terms\n",
    "The ground truth or originating function is as follows:\n",
    "\n",
    "$$ y=f(x)= (20x+3x^2+0.1x^3).sin(x).e^{-0.1x}+\\psi(x) $$\n",
    "\n",
    "$$ {OR} $$\n",
    "\n",
    "$$ y=f(x)= (20x+3x^2+0.1x^3)+\\psi(x) $$\n",
    "\n",
    "$${where,}\\ \\psi(x) : {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Definition of the function with exponential and sinusoidal terms\n",
    "def func_trans(x):\n",
    "    result = (20*x+3*x**2+0.1*x**3)*np.sin(x)*np.exp(-0.1*x)\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Definition of the function without exponential and sinusoidal terms i.e. just the polynomial\n",
    "def func_poly(x):\n",
    "    result = 20*x+3*x**2+0.1*x**3\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Densely spaced points for generating the ideal functional curve\n",
    "x_smooth = np.array(np.linspace(x_min,x_max,501))\n",
    "\n",
    "# Use one of the following\n",
    "y_smooth = func_trans(x_smooth)\n",
    "#y_smooth = func_poly(x_smooth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Linearly spaced sample points\n",
    "X=np.array(np.linspace(x_min,x_max,N_points))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Added observational/measurement noise\n",
    "noise_x = np.random.normal(loc=noise_mean,scale=noise_sd,size=N_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Observed output after adding the noise\n",
    "y = func_trans(X)+noise_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Ideal y</th>\n",
       "      <th>Sin_X</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.588211</td>\n",
       "      <td>0.841471</td>\n",
       "      <td>14.742008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.242424</td>\n",
       "      <td>24.804373</td>\n",
       "      <td>0.946569</td>\n",
       "      <td>13.831236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.484848</td>\n",
       "      <td>31.466432</td>\n",
       "      <td>0.996309</td>\n",
       "      <td>26.512902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.727273</td>\n",
       "      <td>36.577161</td>\n",
       "      <td>0.987783</td>\n",
       "      <td>39.917237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.969697</td>\n",
       "      <td>39.197081</td>\n",
       "      <td>0.921489</td>\n",
       "      <td>48.319864</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X    Ideal y     Sin_X          y\n",
       "0  1.000000  17.588211  0.841471  14.742008\n",
       "1  1.242424  24.804373  0.946569  13.831236\n",
       "2  1.484848  31.466432  0.996309  26.512902\n",
       "3  1.727273  36.577161  0.987783  39.917237\n",
       "4  1.969697  39.197081  0.921489  48.319864"
      ]
     },
     "execution_count": 366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the values in a DataFrame\n",
    "df = pd.DataFrame(data=X,columns=['X'])\n",
    "df['Ideal y']=df['X'].apply(func_trans)\n",
    "df['Sin_X']=df['X'].apply(math.sin)\n",
    "df['y']=y\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the function(s), both the ideal characteristic and the observed output (with process and observation noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x294706af0f0>]"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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SAPbvf5zs7HsYM+YFhg8frUmcB7liDJyItAV6Y634m2SM2WVv2o21uB9Yyd2O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\nFUlEQVSEEEIIIRxGAjghhBBCCIf5/ylJlRu2hBYfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294706af7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X','y',title='True process and measured samples\\n',\n",
    "                grid=True,edgecolors=(0,0,0),c='blue',s=60,figsize=(10,6))\n",
    "plt.plot(x_smooth,y_smooth,'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import scikit-learn librares and prepare train/test splits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import LassoCV\n",
    "from sklearn.linear_model import RidgeCV\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df[['X','Sin_X']], df['y'], test_size=test_set_fraction)\n",
    "\n",
    "#X_train=X_train.reshape(X_train.size,1)\n",
    "#y_train=y_train.reshape(y_train.size,1)\n",
    "#X_test=X_test.reshape(X_test.size,1)\n",
    "#y_test=y_test.reshape(y_test.size,1)\n",
    "\n",
    "#X_train=X_train.reshape(-1,1)\n",
    "#y_train=y_train.reshape(-1,1)\n",
    "#X_test=X_test.reshape(-1,1)\n",
    "#y_test=y_test.reshape(-1,1)\n",
    "\n",
    "from sklearn import preprocessing\n",
    "X_scaled = preprocessing.scale(X_train)\n",
    "y_scaled = preprocessing.scale(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model with LASSO/Ridge regularization (pipelined) with lineary spaced samples\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Regression model parameters\n",
    "ridge_alpha = tuple([10**(x) for x in range(-3,0,1) ]) # Alpha (regularization strength) of ridge regression\n",
    "# Alpha (regularization strength) of LASSO regression\n",
    "lasso_eps = 0.0001\n",
    "lasso_nalpha=20\n",
    "lasso_iter=5000\n",
    "\n",
    "# Min and max degree of polynomials features to consider\n",
    "degree_min = 2\n",
    "degree_max = 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SDn0zW5p4uSGQOkNwEHCnmS0D5kqaA+wnaR6wiZm9CCDpVmAw8Fjb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294749ecc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TT9cFLD4+AhhlZkuA2ZJmAntJmgNsYGYvAUi6ExgIPF64qNfQtGnQ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\nczn3/wHQvSflc9BItAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29474acea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XnbBPxrTDht7Agm16rH/td4R05S6nDn3nXOG9+NMRGYnlvW5b0vvCB5skFvA7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29474b790f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x29474bac4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HHU1pCWbexUdmzPfo9eP43InDSxWWcx2Sz/1cPLE4VwKjhg2irmtoytzrjeez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\ncc45V3CeXJxzzhWcJxfnnHMF9/+KRlORipbdDwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29474b372e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0i5QJ3a5YpEw0dtoP37dX2rRDRlzPm1v3BDb0w+iKxVLOcurQF5EiuPbatMTy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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29474b37550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0CZ5UXBnLpUN/DzNbXvBInGvjenSpoTYlwSwYc3TafI/fNIEvnTy0WGE51yq5\n3M/FE4tzRTBiSH9qOoSuzH0XvpgxsfQ5dxI/fL1j0x39zpUJv12xc2WiodN+2N690qYdNPw63uza\nA1jfD+NXLHblLKcOfedcEVxzTVpi+bDT5vQ5d9K6xNLAbzfsyl3F3YnSuaqU4bL4g8/8Ox9s2jXj\n7H67YVfustVcNo+PwcCPCfdS6Qn8CNi78KE51wacfXZaYnl7sy3pc+4k3t+0Kwakph2/3bCrBM3e\niVLS48DeZrYivr4AeKAo0TlXrerrYaP0f79df3YXn3Xo1KjMgJ5davx2w66i5NKhvw2wKvF6VSxz\nzrXGIYfAY481Lhs6lAMPOIvPMvSl9OxSw5PnHVKk4JzLj1ySyy3AdEn3xtfDgJsLF5JzVWrFCujc\nOb28vh7atWNEyuVfwJvAXOXK5TyXi4DvAx/Gx/fN7OJCB+ZcVencOT2xjBoVzrJvF/4Nhw3qySXH\nDqRnlxpEqLFccuxAbwJzFSnX81w2AZab2U2Sukvqa2bzCxmYc1Vh0SLo3Tu9vIlLtwwb1NOTiasK\nzdZcJP0GOBcYGYs6ALcWMijnqoKUnljGjfNrgrk2IZeayzHAIOA5ADNbLGnzgkblXCWbNQv2zjBa\n35OKa0NyOUN/Vbz7pAFI2rSwITlXwaT0xPLYY55YXJuTS3K5Q9K1QBdJpxHuSnl9YcNyrsJMnJjx\nLHvM4OCDix6Oc6WWy50o/yDpcGA50B8438weKXhkzlWKTEnllVegvw8hdm1XLh36Y8zsETMbYWa/\nMLNHJI0pRnDOlbM3jju56dqKJxbXxuXSLHZ4hrIj8x2IcxXDDCR2vLPxucSf/9l4Jjy3qERBOVde\nmkwukn4saTawq6QXEo/5wOzihehcGdl333UnPSb1OXcSb3fYbP397p1r47L1ufwDeAi4BDgvUb7C\nzJYWNCrnys2qVdCxY1px6oUm/T4rzgVN1lzM7CMzWwD8CVhqZm+a2ZvAGkn7FytA50pOSkssi7tu\nS59zJ6Vdwdjvs+JckEufyzXAx4nXH8eyVpP0LUlzJK2VNDhl2khJ8yTNlTQkUb6PpNlx2pVSpp5U\n53I3YVYtB45+lL7nPcCBox9Nvy/9++9n7rCvr2f61Bnr7nffwC8y6dx6uSQXxZMoATCzteR+TbKm\nvAgcCzzeaEPSAOAEYDfgCOBqSQ3/wdcApwH94uOIDYzBtWET4hWIa5fVYUDtsjpG3jN7fYKRoHv3\nxgudcMJGyesqAAAUiklEQVS6C036RSadyy6XJPGGpLNYX1s5HXhjQzZqZi8DZKh8DAXGm9lKYL6k\necB+khYAnc3s6bjcLYRL/z+0IXG4tmvs5LmNLm0PULe6njtvmcywvU9NXyDDGfZ+kUnnmpZLzeVH\nwP8AtcAiYH9geIHi6QksTLxexPrbKy/KUJ6RpOGSZkiasWTJkoIE6ipbpo73BWOO5rYrUhLLmDF+\n6RbnWiGXM/TfIzRVtYikfwHbZpg0yszua+n6WsLMrgOuAxg8eLAfGVyaHl1qqI0JZq/Fc5nw95+n\nzTPhuUVeM3GulZpMLpLOMbNLJf2ZeNHKJDM7K9uKzeywVsRTCySvUd4rltXG56nlzrXKiCH9GXnP\nbF7+ffr5wN85/vc82Wcvau6ZzYw3l/LYK0v8/vXOtVC2msvL8e+MYgQSTQT+IekyoAeh4366mdVL\nWi7pAOAZ4HvAn4sYl6sSE2bVMnbyXPZ6+hFevm902vQ+505a97xudT23Pf3Wul9WDZ3+gCcY55rR\nZHIxs/vj35ubmqe1JB1DSA7dgQckPW9mQ8xsjqQ7gJeANcAZZtbQ63o6MA6oIXTke2e+a5GGEWKZ\naitf+uH1vNUlvRU3tcpet7qesZPnenJxrhnZmsXuJ0NzWAMz+3prN2pm9wL3NjHtIuCiDOUzgN1b\nu03nNv7BKbz83JS08gMvmRqe5Hh2vZ+F71zzsjWL/SH+PZbQMd9wa+MTgXcLGZRzeRXPTTkqpXiP\ns8ezvNNmaFkdlx+/FyPvmd1oeLLI/OvKz8J3rnnZmsX+DSDpj2aWPIv+fknF7IdxLmcNfSoNHfAP\nXzuczRe8njZfsm+lR5eadc1cyWW/vGt37p5Z2yjh+Fn4zuUml5MoN5W0o5m9ASCpL+C3OnZlp6FP\npW51PR1Xr+TJkUenzbPHefex3NZftiWZLDKdFDl4h26NEo6PFnMuN7kkl58C0yS9QWgp2AH4YUGj\ncq4VGs66n/uHY+hYv7rxxN13h9mz+W1Kzaa5ZOFn4TvXOrmcRPmwpH7ArrHolXh5FufKyidvv8eC\nK09MK+97zv3MHxNqMZ4snCuOZpOLpE2AnwE7mNlpkvpJ6m9mk5pb1rmikXg+pWj8Hl/hvCPPoqd3\nwDtXdLk0i90EzAQ+H1/XAncCnlxc6c2bB/36pRU3dNh7B7xzpZFLctnJzI6XdCKAmX3q91JxZSHD\n1/CZsdfxszU7Ie+Ad66kckkuqyTVEIf8S9oJ8D4XVzpPPAFf/GJ6uRn7A08WPSDnXKpcLrn/G+Bh\noLek24CpwDkFjcq5pkhpiWXa3yf5ZfGdKzNZk0ts/nqFcJb+ycA/gcFmNq3gkTmXdNttGZvB+pw7\niR/PbZ9+i2LnXEllbRYzM5P0oJkNBB4oUkzONZYhqfzPj29kceetAb+YpHPlKJdmseck7VvwSJxL\ndcEFaYllZfuN6HPupHWJpYFfTNK58pJLh/7+wHfjfew/IV7Pz8z2KGRgrg1buxbat08v/+gjDrl6\nRsarF/vFJJ0rL7nUXIYAOwKHAF8Djo5/ncu/b30rPbEceGDosO/cmRFD+lPTofF0P5fFufKT7X4u\nnYAfATsDs4EbzGxNsQJzbcxnn0FNhtrH6tWw0fqvaaarF/u5LM6Vn2zNYjcDq4H/BxwJDADOLkZQ\nro3ZaSd4443GZaefDlddlXF2vz6Yc+UvW3IZEEeJIekGYHpxQnJtxpIlsPXW6eVr12YcIeacqxzZ\n+lzWXbPcm8Nc3h1xRHpiufLK0LfiicW5ipet5rKnpOXxuYCa+LphtFjngkfnqk9tLfTqlV7uZ9g7\nV1Wy3eY4w1hQ5zbA9tvDwoWNy2bOhL33Lk08zrmCyeU8F+c2zIsvwsCBjcu22AKWLStNPM65gvPk\n4gorU//J/PlM+LADY0c/6sOJnatSuZxE6VzLPfZYemL5/OfBjAkfdmDkPbOpXVaHAbXL6hh5z2y/\n+KRzVcRrLi7/MtVWPvgAunUDwgmQdavrG032i086V1285uLyJ9Nl8U86KYwEi4kFmr7IpF980rnq\nUZKai6SxhOuTrQJeB75vZsvitJHAqUA9cJaZTY7l+wDjgBrgQeBsMx+/WhaautBkXR106pRW3KNL\nDbV+8Unnqlqpai6PALvHKyu/CowEkDQAOAHYDTgCuFpSw1HrGuA0oF98HFHsoF0GF1+cnlh++9tQ\nW8mQWAC/+KRzbUBJai5mNiXx8mngm/H5UGC8ma0E5kuaB+wXL/ff2cyeBpB0CzAMeKh4UbtGVq7M\nnDzq66Fd9t8sfvFJ56pfOXTonwLcHp/3JCSbBoti2er4PLU8I0nDgeEA22+/fT5jdQCnnQbXX9+4\nbNy40L+SI7/4pHPVrWDJRdK/gG0zTBplZvfFeUYBa4Db8rltM7sOuA5g8ODB3i+TLx9+2Khjfh3v\n+nLOpShYcjGzw7JNl3Qy4cZjhyY65muB3onZesWy2vg8tdwVy8EHw7//3bjskUfgsKwfs3OujSrV\naLEjgHOAg8zs08SkicA/JF0G9CB03E83s3pJyyUdADwDfA/4c7HjbpM++gi6dEkv99qKcy6LUo0W\n+wuwOfCIpOcl/RXAzOYAdwAvAQ8DZ5hZw9l2pwPXA/MIw5e9M7/QLr00LbEc+f0r+dyvHvKz6Z1z\nWanaTxUZPHiwzZgxo9RhVJZ33oHttmtUdNHBp/C3/Y9d97pnlxqePO+QYkfmnCsSSTPNbHBrly+H\n0WKunPz853DZZY2KBv7kdlZ03LRRmZ9N75zLxpOLC15/HXbeuXHZuHEc+HZvVvjZ9M65FvJrizn4\n9rcbJ5Zu3cKlW046yc+md861itdc2rJZs9LvAnn//XD00ete+tn0zrnW8OTSFpmF81Yef3x92e67\nh2SzUfpXws+md861lDeLtTXTpoVrfyUTyxNPwOzZGROLc861hh9N2orVq2HAAJg3b33ZkCHw0EOZ\nb+7lnHMbwGsubcG998LGGzdOLLNnw8MPe2JxzhWE11yq2aefQvfu4W+Dk0+Gm24qWUjOubbBay7V\n6m9/g003bZxY5s/3xOKcKwpPLtXmww9DU9fw4evLRo4MI8T69ClZWM65tsWTSzW5+OL0+628+24o\nd865IvI+l2qweDH0TDkP5Yor4OyzSxOPc67N8+RS6c4+G668snHZ8uWw+ealicc55/Bmscr16quh\nbyWZWG69NfSteGJxzpWY11wqjRkcdxzcddf6sm22gTffhI4dSxeXc84leM2lksyYES7dkkwsDz0U\nbu7licU5V0a85lIJ1q6FL3wBnnpqfdmgQfDss9C+fdPLOedciXjNpdxNnRoSSDKxPPUUPPecJxbn\nXNnymku5Wr0a+vULfSkNjj4aJk7064E558qe11zK0Z13hgtNJhPLnDnhRl6eWJxzFcBrLuXkk0+g\nSxdYs2Z92fDhcO21pYvJOedawWsuJTZhVi0Hjn6UXw05AzbbrHFiefNNTyzOuYrkNZcSmjCrljG3\nPslTlx3fqPyV037CrtddXqKonHNuw3lyKaH3R4ziqak3Nyob9H+3sUmPbXmyRDE551w+lKRZTNLv\nJL0g6XlJUyT1SEwbKWmepLmShiTK95E0O067Uqrgnu1Fi0DiB4nEcv5hP6TPuZP4cJMtWLysroTB\nOefchitVn8tYM9vDzPYCJgHnA0gaAJwA7AYcAVwtqeFkjmuA04B+8XFE0aPOh9NPh969172sVzsG\n/PRObtnna+vKenSpKUVkzjmXNyVpFjOz5YmXmwIWnw8FxpvZSmC+pHnAfpIWAJ3N7GkASbcAw4CH\nihf1Bnr5ZRgwoFHRs5dczfc+6Uvd6vp1ZTUd2jNiSP9iR+ecc3lVstFiki6StBD4DrHmAvQEFiZm\nWxTLesbnqeXlzwyGDm2cWHr3hpUr2fe8H3PJsQPp2aUGAT271HDJsQMZNqgyds0555pSsJqLpH8B\n22aYNMrM7jOzUcAoSSOBM4Hf5HHbw4HhANtvv32+Vtty06fD/vs3LpsyBQ4/fN3LYYN6ejJxzlWd\ngiUXMzssx1lvAx4kJJdaoHdiWq9YVhufp5Y3te3rgOsABg8ebE3NVzBr14akMmPG+rL994f//Cdc\n1dg556pcqUaL9Uu8HAq8Ep9PBE6Q1FFSX0LH/XQzextYLumAOErse8B9RQ06V1OmhAtKJhPL9Onw\n9NOeWJxzbUapznMZLak/sBZ4E/gRgJnNkXQH8BKwBjjDzBp6u08HxgE1hI788urMX7UK+vYN97Nv\ncMwxcPfdfj0w51ybI7PitxoV0+DBg21GshaRgwmzahk7eS6Ll9XRo0sNI4b0z94vMn48nHhi47JX\nXoH+PurLOVeZJM00s8GtXd7P0E8xYVYtI++ZvW54cO2yOkbeMxsgPcF8/HH6/epPPx2uuqoYoTrn\nXNnyToAUYyfPbXTeCUDd6nrGTp7beMa//CU9sSxc6InFOefw5JKmqUuvrCt///3Qh/J//7d+4m9/\nG85n6dUr47LOOdfWeHJJ0dSlV3p0qYHzz4fu3RtP+OAD+PWvixCZc85VDk8uKUYM6U9Nh8b3pt/p\nk/d5cuSh8LvfrS/8619DbaVbtyJH6Jxz5c879FM0dNo3jBa7cupVfG1GYtRzp06htrLJJiWK0Dnn\nyp8nlwyGDerJsI2Xwe67N55w113wjW+UJijnnKsgnlwyqa9vnFh23DGct9KhQ+lics65CuJ9Lpm0\nawdfi/dXmToVXn/dE4tzzrWA11wykWDixFJH4ZxzFctrLs455/LOk4tzzrm88+TinHMu7zy5OOec\nyztPLs455/LOk4tzzrm88+TinHMu7zy5OOecy7uqv82xpCXAm6WOI9oKeL/UQRRANe5XNe4TVOd+\n+T4Vxg5m1r352TKr+uRSTiTN2JB7UperatyvatwnqM798n0qT94s5pxzLu88uTjnnMs7Ty7FdV2p\nAyiQatyvatwnqM798n0qQ97n4pxzLu+85uKccy7vPLk455zLO08uBSLpd5JekPS8pCmSeiSmjZQ0\nT9JcSUMS5ftImh2nXSlJpYk+M0ljJb0S9+teSV0S0ypynwAkfUvSHElrJQ1OmVax+5Uk6Yi4D/Mk\nnVfqeFpC0o2S3pP0YqKsm6RHJL0W/3ZNTMv4mZUTSb0lPSbppfjdOzuWV/R+NWJm/ijAA+iceH4W\n8Nf4fADwX6Aj0Bd4HWgfp00HDgAEPAQcWer9SNmnrwAbxedjgDGVvk8xxs8B/YFpwOBEeUXvV2I/\n2sfYdwQ2jvs0oNRxtSD+LwF7Ay8myi4FzovPz8vlu1hOD2A7YO/4fHPg1Rh7Re9X8uE1lwIxs+WJ\nl5sCDSMnhgLjzWylmc0H5gH7SdqOkJCetvBtugUYVtSgm2FmU8xsTXz5NNArPq/YfQIws5fNbG6G\nSRW9Xwn7AfPM7A0zWwWMJ+xbRTCzx4GlKcVDgZvj85tZ//5n/MyKEmgLmNnbZvZcfL4CeBnoSYXv\nV5InlwKSdJGkhcB3gPNjcU9gYWK2RbGsZ3yeWl6uTiH8Yofq2adU1bJfTe1HJdvGzN6Oz98BtonP\nK25fJfUBBgHPUEX7tVGpA6hkkv4FbJth0igzu8/MRgGjJI0EzgR+U9QAW6G5fYrzjALWALcVM7YN\nkct+ucpkZiapIs+pkLQZcDfwEzNbnuy6q+T9Ak8uG8TMDstx1tuABwnJpRbonZjWK5bVsr6ZKVle\nVM3tk6STgaOBQ2OTEJT5PkGLPqukst+vHDW1H5XsXUnbmdnbsZnyvVheMfsqqQMhsdxmZvfE4orf\nrwbeLFYgkvolXg4FXonPJwInSOooqS/QD5geq8LLJR0QRx59DyirX9SSjgDOAb5uZp8mJlXsPjWj\nWvbrWaCfpL6SNgZOIOxbJZsInBSfn8T69z/jZ1aC+LKK35sbgJfN7LLEpIrer0ZKPaKgWh+EXyQv\nAi8A9wM9E9NGEUZ7zCUxyggYHJd5HfgL8QoK5fIgdCIuBJ6Pj79W+j7FGI8htGGvBN4FJlfDfqXs\n41GEEUmvE5oCSx5TC2L/J/A2sDp+TqcCWwJTgdeAfwHdmvvMyukBfIEwyOeFxP/TUZW+X8mHX/7F\nOedc3nmzmHPOubzz5OKccy7vPLk455zLO08uzjnn8s6Ti3POubzz5OLaLEnDJJmkXXOY9+Tkla1b\nsa2DJU1q7fL5Xo9zhebJxbVlJwJPxL/NORlodXJxrq3x5OLapHhNpy8QTsg7IWXaufFeLf+VNFrS\nNwknTd6mcH+eGkkLJG0V5x8saVp8vp+kpyTNkvQfSf2bieNpSbslXk+L62t2PZIukPSLxOsX40UQ\nkfRdSdNjvNdKah8f4+J8syX9tHXvnnPN82uLubZqKPCwmb0q6QNJ+5jZTElHxmn7m9mnkrqZ2VJJ\nZwK/MLMZAGr63mCvAF80szWSDgMuBr6RJY7bgeOA38RrSW1nZjMkdW7hetaR9DngeOBAM1st6WrC\nlbnnEK4UsXucr0uW1Ti3QTy5uLbqROBP8fn4+HomcBhwk8Vrp5lZ6n1EmrMFcHO8tpwBHZqZ/w5g\nCuGipscBd7VyPUmHAvsAz8YkWEO4AOL9wI6S/gw8ELfrXEF4cnFtjqRuwCHAwHhJ8/aASRrRgtWs\nYX2zcqdE+e+Ax8zsmNhENS3bSsysNtac9iDUNn7UgvUkY0jGIeBmMxuZuoCkPYEhcTvHEe7L41ze\neZ+La4u+CfzdzHYwsz5m1huYD3wReAT4vqRNYF0iAlhBuB1tgwWE2gE0bq7agvWXQj85x3huJ1xt\negsze6EF61lAuP0vkvYm3P4WwoUPvylp64Z9kLRD7CNqZ2Z3A79qWNa5QvDk4tqiE4F7U8ruBk40\ns4cJlzefIel5oKHDfBzw14YOfeBC4E+SZgD1ifVcClwiaRa5twzcRRhUcEcL13M30E3SHMLN6F4F\nMLOXCMljiqQXCAlzO8KdC6fF/boVSKvZOJcvflVk55xzeec1F+ecc3nnycU551zeeXJxzjmXd55c\nnHPO5Z0nF+ecc3nnycU551zeeXJxzjmXd/8fF99SAIJQUP0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29478f2a630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_sample_score = []\n",
    "poly_degree = []\n",
    "rmse=[]\n",
    "t_linear=[]\n",
    "import time\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    t1=time.time()\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "                                                                  max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    t2=time.time()\n",
    "    t = t2-t1\n",
    "    t_linear.append(t)\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(test_pred-y_test)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    linear_sample_score.append(test_score)\n",
    "    rmse.append(RMSE)\n",
    "    poly_degree.append(degree)\n",
    "    #print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "       \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.96598512036243933,\n",
       " 0.99569377302537243,\n",
       " 0.99460804969374861,\n",
       " 0.99320423363398702,\n",
       " 0.9940625210985059,\n",
       " 0.99341697009202246,\n",
       " 0.99345239638432847]"
      ]
     },
     "execution_count": 372,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_sample_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x29478e85198>"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IiIhIY2UmcXP3WcAsADMbATzn7iuas0wzux2oAfqZ2VuEGr0fE/rPTTIzgCfd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\nNzMzM7OCcOJmZmZmVhD/H3D8gtP2/NbXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294742d26d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(poly_degree,rmse,lw=3,c='red')\n",
    "plt.title(\"Model complexity (highest polynomial degree) vs. test score\\n\",fontsize=20)\n",
    "plt.xlabel (\"\\nDegree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"Root-mean-square error on test set\",fontsize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_score = pd.DataFrame(data={'degree':[d for d in range(degree_min,degree_max+1)],\n",
    "                              'Linear sample score':linear_sample_score})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best R^2 score for linear polynomial degree models: 0.995693773025\n"
     ]
    }
   ],
   "source": [
    "# Save the best R^2 score\n",
    "r2_linear = max(linear_sample_score)\n",
    "print(\"Best R^2 score for linear polynomial degree models:\",r2_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x294765058d0>"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mNig0OyBxDhuODej2FuDuJo8zE9hD0mRJo0gDCn9TLCBpfN4H8DHg5pwwPAEc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\nmAy/AFIgq5O0X9LLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294742d2320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(poly_degree,linear_sample_score,lw=3,c='red')\n",
    "plt.xlabel (\"\\nModel Complexity: Degree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"R^2 score on test set\",fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1-hidden layer (Shallow) network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "learning_rate = 1e-6\n",
    "training_epochs = 150000\n",
    "\n",
    "n_input = 1  # Number of features\n",
    "n_output = 1  # Regression output is a number only\n",
    "\n",
    "n_hidden_layer = 100 # layer number of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "weights = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_input, n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_hidden_layer, n_output]))\n",
    "}\n",
    "biases = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_output]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf Graph input\n",
    "x = tf.placeholder(\"float32\", [None,n_input])\n",
    "y = tf.placeholder(\"float32\", [None,n_output])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hidden layer with RELU activation\n",
    "layer_1 = tf.add(tf.matmul(x, weights['hidden_layer']),biases['hidden_layer'])\n",
    "layer_1 = tf.sin(layer_1)\n",
    "\n",
    "# Output layer with linear activation\n",
    "ops = tf.add(tf.matmul(layer_1, weights['out']), biases['out'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define loss and optimizer\n",
    "cost = tf.reduce_mean(tf.squared_difference(ops,y))\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:17: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:18: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:19: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:20: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "100%|████████████████████████████████████████████████████████████████████████| 150000/150000 [02:10<00:00, 1150.13it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "import time\n",
    "\n",
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Empty lists for book-keeping purpose\n",
    "epoch=0\n",
    "log_epoch = []\n",
    "epoch_count=[]\n",
    "acc=[]\n",
    "loss_epoch=[]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], \n",
    "                                     test_size=test_set_fraction)\n",
    "\n",
    "X_train=X_train.reshape(X_train.size,1)\n",
    "y_train=y_train.reshape(y_train.size,1)\n",
    "X_test=X_test.reshape(X_test.size,1)\n",
    "y_test=y_test.reshape(y_test.size,1)\n",
    "\n",
    "# Launch the graph and time the session\n",
    "t1=time.time()\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)    \n",
    "    # Loop over epochs\n",
    "    for epoch in tqdm(range(training_epochs)):\n",
    "        # Run optimization process (backprop) and cost function (to get loss value)\n",
    "        _,l=sess.run([optimizer,cost], feed_dict={x: X_train, y: y_train})\n",
    "        loss_epoch.append(l) # Save the loss for every epoch        \n",
    "        epoch_count.append(epoch+1) #Save the epoch count\n",
    "       \n",
    "        # print(\"Epoch {}/{} finished. Loss: {}, Accuracy: {}\".format(epoch+1,training_epochs,round(l,4),round(accu,4)))\n",
    "        #print(\"Epoch {}/{} finished. Loss: {}\".format(epoch+1,training_epochs,round(l,4)))\n",
    "    w=sess.run(weights)\n",
    "    b = sess.run(biases)\n",
    "    yhat=sess.run(ops,feed_dict={x:X_test})\n",
    "t2=time.time()\n",
    "\n",
    "time_SNN = t2-t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2947bfa8ac8>]"
      ]
     },
     "execution_count": 457,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i/KCeTBiUxYCsFB2zkEAoHEQCVln9SVgUbtnPyuJyjvhHn+amJzF+YE8mnJbF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\n/x//idKFTm5blgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2947c030080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_epoch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE error of the shallow neural network: 94.9837638167\n",
      "R^2 value of the shallow neural network: 0.983809646773\n"
     ]
    }
   ],
   "source": [
    "# Total variance\n",
    "SSt_SNN = np.sum(np.square(y_test-np.mean(y_test)))\n",
    "# Residual sum of squares\n",
    "SSr_SNN = np.sum(np.square(yhat-y_test))\n",
    "# Root-mean-square error\n",
    "RMSE_SNN = np.sqrt(np.sum(np.square(yhat-y_test)))\n",
    "# R^2 coefficient\n",
    "r2_SNN = 1-(SSr_SNN/SSt_SNN)\n",
    "\n",
    "print(\"RMSE error of the shallow neural network:\",RMSE_SNN)\n",
    "print(\"R^2 value of the shallow neural network:\",r2_SNN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29479c63dd8>]"
      ]
     },
     "execution_count": 459,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3FxKcuz8GHBH1uzyM0D/oBsLBqj32I4k/+Dyfxyra3/eynHN11P4DJnO/HBqzvLjvZwfR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2947bfb8e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"Predicted vs. actual (test set) for shallow (1-hidden layer) neural network\\n\",fontsize=15)\n",
    "plt.xlabel(\"Actual values (test set)\")\n",
    "plt.ylabel(\"Predicted values\")\n",
    "plt.scatter(y_test,yhat,edgecolors='k',s=100,c='green')\n",
    "plt.grid(True)\n",
    "plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deep Neural network for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import and declaration of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "learning_rate = 1e-6\n",
    "training_epochs = 15000\n",
    "\n",
    "n_input = 1  # Number of features\n",
    "n_output = 1  # Regression output is a number only\n",
    "\n",
    "n_hidden_layer_1 = 30 # Hidden layer 1\n",
    "n_hidden_layer_2 = 30 # Hidden layer 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights and bias variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Store layers weight & bias as Variables classes in dictionaries\n",
    "weights = {\n",
    "    'hidden_layer_1': tf.Variable(tf.random_normal([n_input, n_hidden_layer_1])),\n",
    "    'hidden_layer_2': tf.Variable(tf.random_normal([n_hidden_layer_1, n_hidden_layer_2])),\n",
    "    'out': tf.Variable(tf.random_normal([n_hidden_layer_2, n_output]))\n",
    "}\n",
    "biases = {\n",
    "    'hidden_layer_1': tf.Variable(tf.random_normal([n_hidden_layer_1])),\n",
    "    'hidden_layer_2': tf.Variable(tf.random_normal([n_hidden_layer_2])),\n",
    "    'out': tf.Variable(tf.random_normal([n_output]))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input data as placeholder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf Graph input\n",
    "x = tf.placeholder(\"float32\", [None,n_input])\n",
    "y = tf.placeholder(\"float32\", [None,n_output])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden and output layers definition (using TensorFlow mathematical functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hidden layer with activation\n",
    "layer_1 = tf.add(tf.matmul(x, weights['hidden_layer_1']),biases['hidden_layer_1'])\n",
    "layer_1 = tf.sin(layer_1)\n",
    "\n",
    "layer_2 = tf.add(tf.matmul(layer_1, weights['hidden_layer_2']),biases['hidden_layer_2'])\n",
    "layer_2 = tf.nn.relu(layer_2)\n",
    "\n",
    "# Output layer with linear activation\n",
    "ops = tf.add(tf.matmul(layer_2, weights['out']), biases['out'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent optimizer for training (backpropagation):\n",
    "For the training of the neural network we need to perform __backpropagation__ i.e. propagate the errors, calculated by this cost function, backwards through the layers all the way up to the input weights and bias in order to adjust them accordingly (minimize the error). This involves taking first-order derivatives of the activation functions and applying chain-rule to ___'multiply'___ the effect of various layers as the error propagates back.\n",
    "\n",
    "You can read more on this here: [Backpropagation in Neural Network](https://en.wikipedia.org/wiki/Backpropagation)\n",
    "\n",
    "Fortunately, TensorFlow already implicitly implements this step i.e. takes care of all the chained differentiations for us. All we need to do is to specify an Optimizer object and pass on the cost function. Here, we are using a Gradient Descent Optimizer.\n",
    "\n",
    "Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point.\n",
    "\n",
    "You can read more on this: [Gradient Descent](https://en.wikipedia.org/wiki/Gradient_descent)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define loss and optimizer\n",
    "cost = tf.reduce_mean(tf.squared_difference(ops,y))\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TensorFlow Session for training and loss estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:19: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:20: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:21: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:22: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "100%|██████████████████████████████████████████████████████████████████████████| 15000/15000 [00:12<00:00, 1184.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run: 1 finished. Score: 0.9971303423849963\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 15000/15000 [00:12<00:00, 1175.69it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run: 2 finished. Score: 0.9796439784984272\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 15000/15000 [00:12<00:00, 1208.46it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run: 3 finished. Score: 0.996214441570084\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 15000/15000 [00:13<00:00, 1130.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run: 4 finished. Score: 0.9948990749889024\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 15000/15000 [00:12<00:00, 1190.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run: 5 finished. Score: 0.9919979092138294\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "import time\n",
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Empty lists for book-keeping purpose\n",
    "epoch=0\n",
    "log_epoch = []\n",
    "epoch_count=[]\n",
    "acc=[]\n",
    "loss_epoch=[]\n",
    "r2_DNN = []\n",
    "test_size = []\n",
    "\n",
    "for i in range(5):\n",
    "    X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], \n",
    "                                     test_size=test_set_fraction)\n",
    "\n",
    "    X_train=X_train.reshape(X_train.size,1)\n",
    "    y_train=y_train.reshape(y_train.size,1)\n",
    "    X_test=X_test.reshape(X_test.size,1)\n",
    "    y_test=y_test.reshape(y_test.size,1)\n",
    "    # Launch the graph and time the session\n",
    "    with tf.Session() as sess:\n",
    "        sess.run(init)    \n",
    "        # Loop over epochs\n",
    "        for epoch in tqdm(range(training_epochs)):\n",
    "            # Run optimization process (backprop) and cost function (to get loss value)\n",
    "            #r1 = int(epoch/10000)\n",
    "            #learning_rate = learning_rate-r1*3e-6\n",
    "            #optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)\n",
    "            _,l=sess.run([optimizer,cost], feed_dict={x: X_train, y: y_train})\n",
    "            \n",
    "        yhat=sess.run(ops,feed_dict={x:X_test})\n",
    "\n",
    "    #test_size.append(0.5-(i*0.04))\n",
    "    # Total variance\n",
    "    SSt_DNN = np.sum(np.square(y_test-np.mean(y_test)))\n",
    "    # Residual sum of squares\n",
    "    SSr_DNN = np.sum(np.square(yhat-y_test))\n",
    "    # Root-mean-square error\n",
    "    RMSE_DNN = np.sqrt(np.sum(np.square(yhat-y_test)))\n",
    "    # R^2 coefficient\n",
    "    r2 = 1-(SSr_DNN/SSt_DNN)\n",
    "    r2_DNN.append(r2)\n",
    "    print(\"Run: {} finished. Score: {}\".format(i+1,r2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot R2 score corss-validation results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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itCbeTLm0Y6fM3Dwzt8+qU3tGW6CmS8yTbpJOBU9IZq7OzBdRTte/k9Lyu4ryg+X1wC8i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\nVkEOAs3MzMwqyEGgmZmZWQX9P8yW/EopPUu8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29479f3e0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title(\"\\nR2-score for cross-validation runs of \\ndeep (2-layer) neural network\\n\",fontsize=25)\n",
    "plt.xlabel(\"\\nCross-validation run with random test/train split #\",fontsize=15)\n",
    "plt.ylabel(\"R2 score (test set)\\n\",fontsize=15)\n",
    "plt.scatter([i+1 for i in range(5)],r2_DNN,edgecolors='k',s=100,c='green')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
